Efficient Reasoning via Constrained Optimization in Latent Space
Abstract
Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they still suffer from overthinking, generating redundant reasoning steps which incur substantial token consumption. Existing methods, such as suppressing reflective keywords or forcing shorter reasoning lengths, attempt to mitigate this issue but inevitably truncate necessary steps and induce underthinking, thereby compromising performance. To address this dilemma, we investigate the latent representations and observe that efficient reasoning steps naturally cluster into a concentrated region in latent space, while those deviating from this region tend to produce verbose sequences. To leverage this, we keep reasoning focused within this region via a quadratic program which projects deviating hidden states back into the region. Then we propose a novel training-free framework to achieve efficient reasoning that reduces token generation costs without sacrificing performance. Extensive experiments conducted on four models ranging from 1.5B to 14B, and across six benchmarks in math reasoning, coding, and scientific QA, validate the effectiveness of our method, up to a 12.1\% improvement in accuracy while reducing generated tokens by 11.8\% to 52.8\%. Codes are available at \href{https://github.com/hzn18/Opt4Reasoning}{https://github.com/hzn18/Opt4Reasoning}.
Related
- LASER: Latent Space Adjoint Matching for Support-Constrained Entropy-Regularized Offline RL
- ReAPO: Retry-Aware Policy Optimization for Efficient Exploration in LLM Reasoning
- A Unified Efficient Gradient-Based Heuristic For Box-Constrained Expectation-Related and Risk-Averse Stochastic Optimization Problems
- A Latent-Space Statistical Learning Framework for Semicontinuous Outcomes: Regularized Deviance and Boundary-Stabilized Optimization
- Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures
BibTeX
@misc{hou2026efficient,
title = {{Efficient Reasoning via Constrained Optimization in Latent Space}},
author = {Zhinan Hou and Xingchen Li and Keyou You},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.34181},
eprint = {2609.34181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34181},
}
RIS
TY - UNPB
TI - Efficient Reasoning via Constrained Optimization in Latent Space
AU - Zhinan Hou
AU - Xingchen Li
AU - Keyou You
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2609.34181
UR - https://arxiv.org/abs/2609.34181
AB - Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they still suffer from overthinking, generating redundant reasoning steps which incur substantial token consumption. Existing methods, such as suppressing reflective keywords or forcing shorter reasoning lengths, attempt to mitigate this issue but inevitably truncate necessary steps and induce underthinking, thereby compromising performance. To address this dilemma, we investigate the latent representations and observe that efficient reasoning steps naturally cluster into a concentrated region in latent space, while those deviating from this region tend to produce verbose sequences. To leverage this, we keep reasoning focused within this region via a quadratic program which projects deviating hidden states back into the region. Then we propose a novel training-free framework to achieve efficient reasoning that reduces token generation costs without sacrificing performance. Extensive experiments conducted on four models ranging from 1.5B to 14B, and across six benchmarks in math reasoning, coding, and scientific QA, validate the effectiveness of our method, up to a 12.1\% improvement in accuracy while reducing generated tokens by 11.8\% to 52.8\%. Codes are available at \href{https://github.com/hzn18/Opt4Reasoning}{https://github.com/hzn18/Opt4Reasoning}.
ER -